details

property	value
status	complete
benchmark	kabasci02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.223177 seconds
cpu usage	0.060224
user time	0.030873
system time	0.029351
max virtual memory	113188.0
max residence set size	9288.0

stage attributes

key	value
starexec-result	YES

output

YES Input TRS: 1: p(0()) -> 0() 2: p(s(x)) -> x 3: plus(x,0()) -> x 4: plus(0(),y) -> y 5: plus(s(x),y) -> s(plus(x,y)) 6: plus(s(x),y) -> s(plus(p(s(x)),y)) 7: plus(x,s(y)) -> s(plus(x,p(s(y)))) 8: times(0(),y) -> 0() 9: times(s(0()),y) -> y 10: times(s(x),y) -> plus(y,times(x,y)) 11: div(0(),y) -> 0() 12: div(x,y) -> quot(x,y,y) 13: quot(zero(y),s(y),z) -> 0() 14: quot(s(x),s(y),z) -> quot(x,y,z) 15: quot(x,0(),s(z)) -> s(div(x,s(z))) 16: div(div(x,y),z) -> div(x,times(zero(y),z)) 17: eq(0(),0()) -> true() 18: eq(s(x),0()) -> false() 19: eq(0(),s(y)) -> false() 20: eq(s(x),s(y)) -> eq(x,y) 21: divides(y,x) -> eq(x,times(div(x,y),y)) 22: prime(s(s(x))) -> pr(s(s(x)),s(x)) 23: pr(x,s(0())) -> true() 24: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 25: if(true(),x,y) -> false() 26: if(false(),x,y) -> pr(x,y) 27: zero(div(x,x)) -> x 28: zero(divides(x,x)) -> x 29: zero(times(x,x)) -> x 30: zero(quot(x,x,x)) -> x 31: zero(s(x)) -> if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) Number of strict rules: 31 Direct POLO(bPol) ... failed. Uncurrying p 1: p^1_0() -> 0() 2: p^1_s(x) -> x 3: plus(x,0()) -> x 4: plus(0(),y) -> y 5: plus(s(x),y) -> s(plus(x,y)) 6: plus(s(x),y) -> s(plus(p^1_s(x),y)) 7: plus(x,s(y)) -> s(plus(x,p^1_s(y))) 8: times(0(),y) -> 0() 9: times(s(0()),y) -> y 10: times(s(x),y) -> plus(y,times(x,y)) 11: div(0(),y) -> 0() 12: div(x,y) -> quot(x,y,y) 13: quot(zero(y),s(y),z) -> 0() 14: quot(s(x),s(y),z) -> quot(x,y,z) 15: quot(x,0(),s(z)) -> s(div(x,s(z))) 16: div(div(x,y),z) -> div(x,times(zero(y),z)) 17: eq(0(),0()) -> true() 18: eq(s(x),0()) -> false() 19: eq(0(),s(y)) -> false() 20: eq(s(x),s(y)) -> eq(x,y) 21: divides(y,x) -> eq(x,times(div(x,y),y)) 22: prime(s(s(x))) -> pr(s(s(x)),s(x)) 23: pr(x,s(0())) -> true() 24: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 25: if(true(),x,y) -> false() 26: if(false(),x,y) -> pr(x,y) 27: zero(div(x,x)) -> x 28: zero(divides(x,x)) -> x 29: zero(times(x,x)) -> x 30: zero(quot(x,x,x)) -> x 31: zero(s(x)) -> if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) 32: p(0()) ->= p^1_0() 33: p(s(_1)) ->= p^1_s(_1) Number of strict rules: 31 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #plus(s(x),y) -> #plus(p^1_s(x),y) #2: #plus(s(x),y) -> #p^1_s(x) #3: #pr(x,s(s(y))) -> #if(divides(s(s(y)),x),x,s(y)) #4: #pr(x,s(s(y))) -> #divides(s(s(y)),x) #5: #div(x,y) -> #quot(x,y,y) #6: #zero(s(x)) -> #if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) #7: #zero(s(x)) -> #eq(x,s(0())) #8: #zero(s(x)) -> #plus(zero(0()),0()) #9: #zero(s(x)) -> #zero(0()) #10: #zero(s(x)) -> #plus(0(),zero(0())) #11: #zero(s(x)) -> #zero(0()) #12: #quot(s(x),s(y),z) -> #quot(x,y,z) #13: #eq(s(x),s(y)) -> #eq(x,y) #14: #plus(x,s(y)) -> #plus(x,p^1_s(y)) #15: #plus(x,s(y)) -> #p^1_s(y) #16: #times(s(x),y) -> #plus(y,times(x,y)) #17: #times(s(x),y) -> #times(x,y) #18: #p(s(_1)) ->? #p^1_s(_1) #19: #plus(s(x),y) -> #plus(x,y) #20: #prime(s(s(x))) -> #pr(s(s(x)),s(x)) #21: #p(0()) ->? #p^1_0() #22: #if(false(),x,y) -> #pr(x,y) #23: #divides(y,x) -> #eq(x,times(div(x,y),y)) #24: #divides(y,x) -> #times(div(x,y),y) #25: #divides(y,x) -> #div(x,y) #26: #div(div(x,y),z) -> #div(x,times(zero(y),z)) #27: #div(div(x,y),z) -> #times(zero(y),z) #28: #div(div(x,y),z) -> #zero(y) popout

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all output return to TRS Standard